Prof S Godsill
Timing and Structure
Michaelmas term. 16 lectures.
The aims of the course are to:
- Study more advanced probability theory, leading into random process theory.
- Study random process theory and focus on discrete time methods.
- Introduce inferential methodology, including maximum likelihood and Bayesian procedures, and examples drawn from signal processing. Objectives
As specific objectives, by the end of the course students should be able to:
- By the end of the course students should be familiar with the fundamental concepts of statistical signal processing, including random processes, probability, estimation and inference.
Lectures 1-8: Advanced Probability and Random Processes
Probability and random variables
Sample space, events, probability measure, axioms.
Conditional probability, probability chain rule, independence, Bayes rule.
Random variables (discrete and continuous), probability mass function (pmf), probability density function (pdf), cumulative distribution function, transformation of random variables.
Bivariate: conditional pmf, conditional pdf, expectation, conditional expectation.
Multivariates: marginals, Gaussian (properties), characteristic function, change of variables (Jacobian.)
Definition of a random process, finite order densities.
Stationarity–strict sense, wide sense. Examples: iid process, random-phase sinusoid.
Ergodicity, Central limit theorem.
Response of linear systems to stochastic inputs – time and frequency domain.
Time series models: AR, MA, ARMA
Lectures 9-16: Detection, Estimation and Inference
Basic linear estimation theory: BLUE, MMSE, bias, variance
Least squares, maximum likelihood, Bayesian inference.
The ML/Bayesian linear Gaussian model
Maximum likelihood and Bayesian estimation
Example inference models: frequency estimation, AR model, Estimation of parameters for discrete Markov chain.
Random variables and random number generation
- Understand random variables and functions of random variables and their simulation
- To study the Jacobian as used with random variables
- To experiment with methods for non-uniform random number generation
- Sessions will take place in [Location], during week(s) [xxx].
- This activity involves preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Please refer to Form & conduct of the examinations.
The UK Standard for Professional Engineering Competence (UK-SPEC) describes the requirements that have to be met in order to become a Chartered Engineer, and gives examples of ways of doing this.
UK-SPEC is published by the Engineering Council on behalf of the UK engineering profession. The standard has been developed, and is regularly updated, by panels representing professional engineering institutions, employers and engineering educators. Of particular relevance here is the 'Accreditation of Higher Education Programmes' (AHEP) document which sets out the standard for degree accreditation.
The Output Standards Matrices indicate where each of the Output Criteria as specified in the AHEP 3rd edition document is addressed within the Engineering and Manufacturing Engineering Triposes.
Last modified: 20/05/2021 07:39